Does anyone happen to know (and ideally have a cite for) whether it is
known if the Hahn Banach theorem implies the existence of a subset of R
without the Baire Property (in ZF say)? I'm presuming it does, as it proves
the existence of a non-measurable subset of R, but I can't seem to find a
reference one way or the other.
(Sorry for the rather analysis-like question, but I think it really is
still FOM. Especially as it's entirely possible that the only way to answer
it is to construct a certain model of set theory!)
Thanks,
David R. MacIver